When such petition is presented for hearing, the legislative authority of each county in which the territory proposed to be annexed is located shall hear the petition or may adjourn the hearing from time to time not exceeding one month in all, and any person, firm, or corporation may appear before the county legislative authority and make objections to the proposed boundary lines or to annexation of the territory described in the petition. Upon a final hearing each county legislative authority shall make such changes in the proposed boundary lines within the county as it deems to be proper and shall establish and define such boundaries and shall find whether the proposed annexation as established by the county legislative authority to the district will be conducive to the public health, welfare and convenience and will be of special benefit to the land included within the boundaries of the territory proposed to be annexed to the district. No lands which will not, in the judgment of the county legislative authority, be benefited by inclusion therein, shall be included within the boundaries of the territory as so established and defined. No change shall be made by the county legislative authority in the boundary lines, including any territory outside of the boundary lines described in the petition. No person having signed such petition shall be allowed to withdraw such person's name therefrom after the filing of the petition with the board of commissioners.
Upon the entry of the findings of the final hearing each county legislative authority, if it finds the proposed annexation to be conducive to the public health, welfare, and convenience and to be of special benefit to the land proposed to be annexed and included within the boundaries of the district, shall give notice of a special election to be held within the boundaries of the territory proposed to be annexed to the district for the purpose of determining whether the same shall be annexed to the district. The notice shall particularly describe the boundaries established by the county legislative authority, and shall state the name of the district to which the territory is proposed to be annexed, and the notice shall be published in a newspaper of general circulation in the territory proposed to be annexed at least once a week for a minimum of two successive weeks prior to the election and shall be posted for the same period in at least four public places within the boundaries of the territory proposed to be annexed, which notice shall designate the places within the territory proposed to be annexed where the election shall be held, and the proposition to the voters shall be expressed on ballots which contain the words:
For Annexation to District
or
Against Annexation to District
The county legislative authority shall name the persons to act as judges at that election.